Plastic mechanisms database for thin-walled cold-formed steel members in compression and bending

Short members of thin-walled cold-formed (TWCF) steel sections, in compression and bending, fail by forming local plastic mechanisms. Taking into account the localised buckling pattern, the collapse of slender members, due to the interaction between local and overall buckling modes, is always characterised by local plastic mechanism failure mode. Based on these two observations, the ultimate strength in interactive buckling of these members can be regarded as an interaction between localised plastic mode and overall elastic one.The yield line mechanism method has been widely used to predict the sectional strength (e.g. local) of thin-walled cold-formed steel members that involve failure mode characterized by local collapse mechanisms. This method can be also used to study post-collapse behaviour and to evaluate the load-carrying capacity, ductility and energy absorption.This paper is based on previous studies and some latest investigations of authors, as well as the literature collected data. It represents an attempt to make an inventory, classify and range geometrical and analytical models for the local-plastic mechanisms aiming to characterize the ultimate capacity of some of the most used cold-formed steel sections in structural applications.     

Selected Problems of Collapse Behaviour Analysis of Structural Members Built from Strain-Hardening Material

In this work the results of the collapse behaviour analysis of thin-walled, trapezoidal box-section beams subject to pure bending are presented. The analysis emphasizes two problems: the strain-hardening effect in the structural material and different modes of stress distribution at yield lines, inducing different plastic moment capacities at those lines. The problem is solved by means of the energy method, based upon the plastic mechanism approach, applied for thin-walled structures. Two theoretical models of plastic mechanisms of failure are discussed.     

The buckling of a pin-ended column of rectangular cross-section and strain hardening mild steel into the large-deflection range

This paper is essentially a study of the effect of strain hardening on the behaviour of a mild-steel pin-ended column. A perfectly elastic-perfectly plastic column can develop theoretically a plastic hinge with infinite curvature at its midpoint. Strain hardening ‘blocks’ the development of sharp kinks. Instead, the central part of the column has a finite curvature. While this phenomenon is probably not important for relatively long columns, in the short columns, like those which form parts of a local plastic mechanism in a thin-walled structure, the effect is to increase the load-carrying and energy-absorbing capacities of the structure by a large factor. The analysis is carried out by using numerical techniques, and the results compare quite favourably with experimental measurements. Finally, a study of the sensitivity of strut behaviour to changes in the shape of the strain-hardening stress-strain diagram is carried out.     

The Ultimate Load Analysis of Thin-Walled Concrete Box Beams

This paper considers the determination of the ultimate load analysis of thin-walled concrete box beams. It can be shown that rigid plastic analysis may be used to determine a yield criterion for the reinforced concrete elements forming a box. Consideration is given to the various collapse mechanisms which are possible.

The paper presents some theoretical results and compares them with the results obtained from an experimental programme conducted on four model box structures. Allowance is made for the difference in material behaviour between micro-concrete and prototype concrete.     

Assessment of the load-carrying capacity of multi-span masonry arch bridges using fibre beam elements

An approach that makes use of non-linear beam elements with fibre cross-section has been used for modelling the ultimate behaviour of multi-span masonry arch bridges. The proposed approach proves able to take into account the interaction among the spans and the non-linear material behaviour with low computational effort. In order to validate the use of the model for the assessment of masonry arch bridges, the load-carrying capacity for typical multi-span railway bridges has been evaluated and the results compared to experimental results and to currently used limit analysis methods. It is shown that, by parity of constitutive assumption, the method provides the same results as limit analysis, both in terms of maximum load prediction and hinges position at collapse; however, taking the effective ductility capacity into account, a strong reduction in load-carrying capacity with respect to classical limit analysis was found, depending on rise-to-span arch ratio, piers slenderness and backfill height. The approach is then applied to a seven span viaduct of the Italian railway network, for which the effective mechanical properties of masonry were identified through an experimental campaign on brickwork samples according to the effective material properties surveyed on site.     

Post-buckling behaviour and DSM design of web-stiffened lipped channel columns with distortional and local mode interaction

This paper examines the design and load-carrying capacity of fixed-ended web-stiffened lipped channel columns eroded by mode interaction behaviour combined with distortional and local deformations. Initially, the paper presents the results of an experimental investigation of compressive tests on web-stiffened lipped channel columns fabricated from cold-formed mild steel with a thickness of 1.50 mm, which is aimed at determining their failure load-carrying capacity; the experimental investigation also aims to provide experimental evidence of the occurrence of such coupling phenomena concerning distortional and local modes, namely, local-distortional interaction and distortional-local interactive failures. Then, the paper examines the ultimate strength data of experimental columns, both reported in this paper and collected from the literature, and concludes that the current direct strength method (DSM) provides very unsafe predictions concerning such a detrimental interaction nature. Next, two DSM-based design approaches, namely, the nominal strength against local-distortional (NLD) and distortional-local (NDL) procedures, are presented and evaluated on the basis of all available experimental ultimate strength data. Finally, proposals and design considerations based on the DSM-shape for the thin-walled cold-formed steel sections, which fail in mixed modes of distortional and local buckling, are presented.     

GBT-based first-order analysis of elastic-plastic thin-walled steel members exhibiting strain-hardening

This paper addresses the development and illustrates the application of a generalised beam theory (GBT) formulation intended to perform first-order elastic-plastic analyses of thin-walled members made of isotropic non-linear materials exhibiting strain-hardening. After presenting an overview of the main concepts and procedures involved in the above GBT formulation, its application is illustrated through the analysis of (i) simply supported Z-section beams and (ii) fixed-ended lipped channel beams. In both cases, a bilinear elastic-plastic material model is adopted, which exhibits three strain-hardening levels, namely E_sh = 0 (perfectly plastic model), E_sh = E/100 and E_sh = E/50. The results presented and discussed consist of equilibrium paths, modal participation diagrams, displacement profiles, beam deformed configurations and stress diagrams and contours. For validation purposes, most of the GBT results are compared with values obtained from shell finite element analyses ? with a few relatively minor exceptions, a very good correlation is always found. Finally, the paper closes with some remarks concerning the influence of the strain-hardening slope on the structural behaviour of thin-walled steel beams.     

屈服强度550MPa高强冷弯薄壁型钢结构轴心受压构件可靠度分析

本文采用二阶矩概率法,考虑强度、截面几何参数、计算模式、外荷载等不定因素的影响,针对屈服强度550MPa高强冷弯薄壁型钢轴心受压构件的可靠度进行了分析,并考虑材料特性,在已有试验的基础上对其承载力计算方法、目标可靠指标及强度设计指标的合理选取进行了研究。结果表明,在按厚度分类合理确定高强冷弯薄壁型钢的强度设计指标后,可依据现行的《冷弯薄壁型钢结构技术规范》(GB 50018—2002)给定的考虑板组稳定计算截面有效宽厚比的方法对其轴心受压构件的极限承载力进行有效分析,并满足预定设计可靠指标的要求。     

Experimental tests of stability and load carrying capacity of compressed thin-walled multi-cell columns of triangular cross-section

In the work the results of experimental tests of stability and ultimate load of compressed thin-walled columns of triangular cross-sections are presented. The tests have been conducted in order to prove that by substituting a single-cell cross-section by multi-cell one (at constant value of area) it is possible to exploit the material strength properties more efficiently. The experiments allow for verification of calculation methods proposed earlier and for the analysis of the inevitable imperfections’ influence on the behaviour and load carrying capacity of the tested models.     

屈服强度550MPa高强冷弯薄壁型钢轴压构件承载力设计

高强冷弯薄壁型钢结构在国外低层住宅和门式刚架体系中应用较广,国内已开始采用,但尚无相应设计规范可依。针对屈服强度550MPa高强钢材冷弯薄壁型钢结构常用的轴压构件的承载力设计方法进行了研究,包括其承载力计算模式及设计可靠度分析,并据此提出了相应的设计方法。最后,通过国内外现有相关试验数据的分析,验证了所提出的强度设计指标及承载力设计方法的合理性与可靠性。     

Interaction of global and local buckling in welded RHS compression members

This paper presents the results of a research project analysing some aspects of the stability failure of thin-walled compression members that are likely to exhibit combined global and local buckling. In particular, the influence of various imperfections, namely residual stresses due to welding and local as well as global geometrical defects, on the load-carrying capacity was subjected to detailed experimental and numerical investigations. The insights obtained into the structural behaviour led to a proposal for modification of the non-dimensional slenderness used in the global buckling verification, and to the recommendation of a shift from the currently applied European buckling curve to a more favourable one in the case of non-stiffened members with welded box sections subjected to pure compression.     

Analysis and design reliability of axially compressed members with high-strength cold-formed thin-walled steel

High-strength cold-formed thin-walled steel has been widely used in developed countries in the last several years. However, the application and popularization of the new materials in China is still very limited, and there are no related provisions in current design codes for reference in engineering practice. In this paper, considering the effects of the variations from material strength in structural members, geometrical parameters of sections, analysis methods for limit load-carrying capacity and external loadings, the second-order moment probability method was used for conducting the design reliability analysis of 550 MPa high-strength cold-formed thin-walled steel structures, from which the reasonable target reliability index, the corresponding resistance partial coefficient and the design strength values were discussed and proposed. Existing experimental data related have been collected and used to demonstrate the suitability and reasonability of the proposed results, which shows that, with reasonable determination of the design strength value of 550 MPa high-strength cold-formed thin-walled steel sections, the effective width-to-thickness ratio method considering coupling stability of plates recommended by “Technical Code of Cold-formed Thin-Walled Steel Structures (GB50018-2002)” can be efficiently used to estimate the load-carrying capacities of the axially compressed elements of high-strength cold-formed thin-walled steel structures, and well satisfy the target reliability index in structural design.     

Comparative experimental study of hot-rolled and cold-formed rectangular hollow sections

Square and rectangular hollow sections are generally produced either by hot-rolling or cold-forming. Cross-sections of nominally similar geometries, but from the two different production routes may vary significantly in terms of their general material properties, geometric imperfections, residual stresses, corner geometry and material response and general structural behaviour and load-carrying capacity. In this paper, an experimental programme comprising tensile coupon tests on flat and corner material, measurements of geometric imperfections and residual stresses, stub column tests and simple and continuous beam tests is described. The results of the tests have been combined with other available test data on square and rectangular hollow sections and analysed. Enhancements in yield and ultimate strengths, beyond those quoted in the respective mill certificates, were observed in the corner regions of the cold-formed sections—these are caused by cold-working of the material during production, and predictive models have been proposed. Initial geometric imperfections were generally low in both the hot-rolled and cold-formed sections, with larger imperfections emerging towards the ends of the cold-formed members—these were attributed largely to the release of through thickness residual stresses, which were themselves quantified. The results of the stub column and simple bending tests were used to assess the current slenderness limits given in Eurocode 3, including the possible dependency on production route, whilst the results of the continuous beam tests were evaluated with reference to the assumptions typically made in plastic analysis and design. Current slenderness limits, assessed on the basis of bending tests, appear appropriate, though the Class 3 slenderness limit, assessed on the basis of compression tests, seems optimistic. Of the features investigated, strain hardening characteristics of the material were identified as being primarily responsible for the differences in structural behaviour between hot-rolled and cold-formed sections.     

高强冷弯薄壁型钢卷边槽形截面构件设计可靠度分析

基于已有的承载力试验研究结果,对屈服强度550MPa高强冷弯薄壁型钢中常用的卷边槽形截面轴压构件和偏压构件的计算模式不定性进行了分析,并统计分析了高强冷弯薄壁型钢强度不定性、几何特性不定性。在此基础上,采用改进一次二阶矩方法,按现有规范的抗力分项系数要求,计算了高强冷弯薄壁型钢卷边槽形截面轴压构件和偏压构件不同可能荷载组合下的可靠指标。结果表明：对于宽厚比符合规范要求的屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件和偏压构件,按现有规范的抗力分项系数计算得到的可靠指标均能满足目标可靠指标的要求,证明了所采用的承载力计算方法的适用性;但对于宽厚比超出规范要求的轴压和偏压构件,计算得到的可靠指标不能满足目标可靠指标的要求。     

Application of surfaces of ultimate strength for thin-walled beams

This paper deals with the problem of ultimate load-carrying capacity of thin-walled sections subject to combined load. That has direct implementation in sizing and design of thin-walled structures. It is solved using the ultimate strength method based on the theory of plastic analysis of structures. It is assumed that the elastic strains are negligible in comparison to the plastic strains and that justifies the application of a fully plastic model. The following problems have to be analyzed before the sizing and design is completed:

• Load vectors and load components

• Locations of the plastic neutral axes

• The surface of ultimate strength

The most important achievement presented in this paper is an improvement for the location of the plastic neutral axis. Until now, the position of the plastic neutral axis has been localized by iterations, starting with the position from the elastic model. That led, in some cases, to a statically inadmissible model and lack of equilibrium in case of asymmetric sections or asymmetric loads.A successful solution to the problem consists in covering the whole section with a mesh of plastic neutral axes and a cluster of corresponding points on the surface of ultimate strength.One of the points on the surface has load components in proportion with the load vector. The corresponding location of the plastic neutral axis is precisely the one we are seeking.The load vector may be extended to pierce one of the triangles that the surface is made of. The coordinates of the point where the load vector is piercing the triangle is a weighted-average of the coordinates of three vertices of the triangle. The same weight is used to localize the plastic neutral axis corresponding to the piercing point of the surface.     

Ultimate load-carrying capacity of cold-formed thin-walled columns with built-up box and I section under axial compression

The use of cold-formed thin-walled steel structures has increased in recent years, and some built-up section members are motivated and also widely used for their excellent structural behaviors. In this paper, a series of axially-compressed tests on built-up box section members composed of two C-section by self-drilling screws at flanges are conducted. The differences of global, local and distortional buckling behaviors between members with built-up and single sections are investigated at first. Then the effects of installation error and fastener spacing on ultimate load-carrying capacity of built-up members are analyzed. A strength estimation method for built-up members under axial compression is proposed based on the experimental investigation in this paper, as well as some existing experiments, and corresponding numerical analysis studies. Finally, the predicted capacity obtained by using the proposed strength estimation method is compared with experimental results and the nominal axial strength determined according to the AISI provisions, by which the suitability and accuracy of the proposed strength estimation method have been established.     

薄壁短柱轴压承载力的非线性有限元分析与计算

利用ANSYS8.1有限元程序对冷弯薄壁帽形截面及卷边槽钢短柱的承载力进行了非线性有限元分析。分析中考虑了材料非线性和初始几何缺陷的影响,提出了合理的有限元分析模型与网格划分密度,分析结果与试验资料吻合较好。此外,分别利用传统的有效宽度法和新兴的直接强度法计算了短柱段的极限承载力,并对翼缘宽厚比超过规范限值的情况提出了计算建议。两种方法除在部分截面的分析中得到较为保守的结果外,其余均与试验值比较接近。直接强度法计算上更加简便,且精度高于有效宽度法,是计算薄壁构件承载能力非常有效的新方法。     

Progressive collapse analysis of thin-walled box columns

Box columns are often used as main strength members of various types of thin-walled structures such as ships, ship-shaped offshore structures, and aerospace structures. Until and after the ultimate limit state is reached, box columns exhibit highly nonlinear structural behavior in terms of geometrical and material aspects. In particular, the effects of local buckling, global buckling, and their interaction play a significant role in the resulting consequences of box columns under extreme actions. In order to calculate the maximum load-carrying capacity of box columns, it is thus highly required to perform the progressive collapse analysis to take into account progressive failures of individual components and their interacting effects. The aim of the present study is to demonstrate a method that is useful for the progressive collapse analysis of thin-walled box columns in terms of computational efficiency and accuracy. Theoretical outline of the method is addressed. Short, medium and long box columns in length are studied in terms of interacting effects between local component failure modes and global system failure modes. The effect of unloaded edge conditions of individual plate elements is also studied. A comparison of the method with more refined nonlinear finite element method computations is made.     

高强冷弯薄壁型钢卷边槽形截面轴压构件试验研究及承载力分析

对63根屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件进行试验研究,分析了构件的屈曲模式和极限承载力,并将参考AISI规范、澳洲规范和北美规范及我国现行行业标准《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）计算的构件承载力与试验结果进行分析比较。在此基础上,对高强超薄壁型钢卷边槽形截面轴压构件的承载力合理计算模式进行研究。结果表明：高强超薄壁型钢卷边槽形截面轴压构件在宽厚比较大时会出现畸变屈曲模式;采用等效板件方法计算加劲板件有效宽度后,我国《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）适用于屈曲强度550MPa、厚度小于2.00mm的冷弯薄壁型钢卷边槽形截面构件承载力计算。     

Recent developments in the buckling and nonlinear analysis of thin-walled structural members

This paper describes recent work performed at the University of Sydney to develop buckling and nonlinear analyses of thin-walled structural members undergoing local, distortional and overall buckling. The analyses are based on the finite strip method of structural analysis and include elastic and inelastic buckling and the full nonlinear response with both post-local buckling and plasticity. Two variations of the finite strip method have been used, these being the semi-analytical and spline finite strip methods. A nonlinear beam-column analysis based on the influence coefficient method for including the local buckling behaviour in the overall member response is also described.

The analytical methods are compared with tests performed at the University of Sydney on cold-formed rectangular hollow sections, welded I-sections, welded channel sections and cold-formed channel sections. Spatial plastic collapse mechanismsdeveloped for the welded sections described above are also compared with the post-ultimate response of the test sections.